Question

An infinite number of particles each of mass 1 kg are placed on the positive x axis at 1m 2m 4m 8m...... From the origin the magnitude of the resultant gravitational force on 1 kg mass kept at the origin is

Answer 1

We can see here that the particles are kept at distances which are in an increasing GP.

Assume a particle at distance of 2^(x-1) m.

=>Grav. force=G*1*1/2^(2x-2)

=>Net grav. force=G*1*1*(1+(1/4)+(1/16)+.......) [i.e. it is an infinite GP]

                            =G*1*1(1/(1-(1/4))

                             =4G/3 newtons

where G-gravitational constant.

Answer 2

Answer:

4G/3

Explanation:

gravitational intensity=GM(1/r1^2+1/r2^2+.........)

G*1(1+1/4+1/8+1/16.......)

infinite gp

so, 4/3*G=4G/3